Method and apparatus for encrypting data in a wireless communication system

ABSTRACT

In a communications system, a method of transforming a set of message signals representing a message comprising the steps of first encoding one of the set of message signals in accordance with a first keyed transformation, a second encoding of the one of the set of message signals in accordance with at least one additional keyed transformation, a third encoding of the one of the set of message signals in accordance with a self inverting transformation in which at least one of the set of message signals is altered, a fourth encoding of the one of the set of message signals in accordance with at least one additional inverse keyed transformation wherein each of the at least one additional inverse keyed transformation is a corresponding inverse of at least one additional keyed transformation, and fifth encoding the one of the set of message signals in accordance with first inverse keyed transformation wherein the first inverse keyed transformation is the inverse of the first keyed transformation.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional of U.S. patent application Ser. No.10/814,065, filed Mar. 30, 2004, allowed, which is a continuation ofU.S. Pat. No. 6,768,797, issued Jul. 27, 2004, which is a continuationof U.S. patent application Ser. No. 10/081,750, filed Feb. 21, 2002,pending, which is a continuation of U.S. Pat. No. 6,385,316, issued May7, 2002, which is a continuation of U.S. Pat. No. 6,075,859, issued Jun.13, 2000, all assigned to the assignee hereof and hereby expresslyincorporated herein.

BACKGROUND OF THE INVENTION

I. Field of the Invention

The present invention relates to communications systems. Moreparticularly, the present invention relates to a novel and improvedmethod for encrypting data for security in wireless communicationsystems.

II. Description of the Related Art

In a wireless communication system, it is desirable for the serviceprovider to be able to verify that a request for service from a remotestation is from a valid user. In some current cellular telephonesystems, such as those deploying the AMPS analog technology, noprovision is made to deter unauthorized access to the system.Consequently, fraud is rampant in these systems. One fraudulent meansfor obtaining service is known as cloning, in which an unauthorized userintercepts the information necessary to initiate a call. Subsequently,the unauthorized user can program a mobile telephone using theintercepted information and use that telephone to fraudulently receivetelephone service.

To overcome these and other difficulties, many cellular telephonesystems have implemented authentication schemes such as thatstandardized by the Telecommunications Industry Association (TIA) inEIA/TIA/IS-54-B. One facet of this authentication scheme is encryptionof information, transmitted over the air, that is required to receiveservice. This information is encrypted using the Cellular MessageEncryption Algorithm (CMEA). The CMEA algorithm is disclosed in U.S.Pat. No. 5,159,634, entitled “CRYPTOSYSTEM FOR CELLULAR TELEPHONY”,incorporated by reference herein.

Several major weaknesses have been discovered in CMEA which allowencrypted information to be deciphered using current standardcomputational equipment in a relatively short period of time. Theseweaknesses will be thoroughly outlined hereinafter followed by adescription of the present invention which overcomes these weaknesses.CMEA has been published on the Internet, hence these weaknesses are openfor discovery by anyone with an interest in doing so. Thus, a newalgorithm for encryption is desirable to replace CMEA to avoid theinterception and fraudulent use of authentication information necessaryto initiate cellular service.

SUMMARY OF THE INVENTION

The present invention is a novel and improved method for dataencryption. The present invention is referred to herein as BlockEncryption Variable Length (BEVL) encoding, which overcomes theidentified weaknesses of the CMEA algorithm. The preferred embodiment ofthe present invention has the following properties:

-   -   Encrypts variable length blocks, preferably at least two bytes        in length;    -   Self-inverting;        -   Uses very little dynamic memory, and only 512 bytes of            static tables;    -   Efficient to evaluate on 8-bit microprocessors; and        -   Uses a 64 bit key, which can be simply modified to use a            longer or shorter key.

The first weakness identified in CMEA is that the CAVE (CellularAuthentication Voice Privacy and Encryption) table used for tablelookups is incomplete. It yields only 164 distinct values instead of256. The existence of a large number of impossible values makes itpossible to guess return values of tbox( ) or key bytes, and verify theguesses. This first weakness is mitigated in the present invention byreplacing the CAVE table with two different tables chosen to eliminatethe exploitable statistical characteristics of the CAVE table. Thesetables, called t1box and t2box, are strict permutations of the 256 8-bitintegers, where no entry appears at its own index position. In addition,t1box[i] does not equal t2box[i], for all values of i. These two tableswere randomly generated with candidates being discarded which did notmeet the above criteria.

The second weakness of CMEA is the repeated use of the value of afunction called tbox( ), evaluated at zero. The value tbox(0) is usedtwice in the encryption of the first byte. This makes it possible toguess tbox(0) and use the guess in determining other information aboutthe ciphering process, notably the result of the first step of CMEA forthe last byte, and the arguments of the two values of tbox( ) used inencrypting the second byte. It also makes it possible, through achosen-plaintext attack, to determine tbox( ) by trying variousplaintext values until a recognized pattern appears in the ciphertext.This second weakness is mitigated by changing the self-invertingprocedures used in CMEA to a preferred set of procedures providingbetter mixing. This is done by introducing a second pass using adifferent table (t2box). In this situation there are two values of tbox() derived from different tables with equal significance which serve tomask each other.

A related weakness in CMEA is that information gathered from analyzingtexts of different lengths can generally be combined. The use of thesecond critical tbox( ) entry in BEVL depends on the length of themessage and makes combining the analysis of different length texts lessfeasible.

A third weakness discovered in CMEA is incomplete mixing of upper bufferentries. The last n/2 bytes of the plaintext are encrypted by simplyadding one tbox( ) value and then subtracting another value, theintermediate step affecting only the first half of the bytes. Thedifference between ciphertext and plaintext is the difference betweenthe two values of tbox( ). BEVL addresses this third weakness byperforming five passes over the data instead of three. The mixing,performed by CMEA only in the middle pass, is done in the second andfourth passes which mix data from the end of the buffer back toward thefront. The middle pass of CMEA also guarantees alteration of at leastsome of the bytes to ensure that the third pass does not decrypt. In animproved manner, BEVL achieves this goal in the middle pass by making akey dependent transformation of the buffer in such a way that at most asingle byte remains unchanged.

CMEA's fourth weakness is a lack of encryption of the least significantbit (LSB) of the first byte. The repeated use of tbox(0) and the fixedinversion of the LSB in the second step of CMEA results in the LSB ofthe first byte of ciphertext being simply the inverse of the LSB of thefirst byte of plaintext. BEVL avoids this fourth weakness through a keydependent alteration of the buffer during the middle pass which makesthe LSB of the first byte unpredictable on buffers of two bytes or morein length.

A fifth weakness of CMEA is that the effective key size is 60 ratherthan 64 bits. As such, each key is equivalent to 15 others. BEVLincreases the number of table lookups while decreasing the number ofarithmetic operations, ensuring that all 64 bits of the key aresignificant.

Finally, CMEA's tbox( ) function can be efficiently compromised by ameet-in-the-middle attack. Once four tbox( ) values are derived, themeet-in-the-middle attack can be accomplished with space and timerequirements on the order of 2̂30, independent of the composition of theCAVE table. BEVL addresses this in a number of ways. The construction ofthe tbox( ) function recovers two unused bits of the key. The repetitionof the combination with the least 8 bits of the encryption key at boththe beginning and end of tbox( ) means that the minimum computation andspace should be increased by eight bits. Since there are two sides ofeach table, and two different tables, the minimum complexity should beincreased by another two bits, leading to a minimum space and timerequirement on the order of 2̂42. Further, the meet-in-the-middle attackon CMEA requires the recovery of at least some of the tbox( ) entries.This is made more difficult using BEVL, which requires simultaneousattacks on two separate sets of tbox( ) values, which tend to disguiseeach other.

BRIEF DESCRIPTION OF THE DRAWINGS

The features, objects, and advantages of the present invention willbecome more apparent from the detailed description set forth below whentaken in conjunction with the drawings in which like referencecharacters identify correspondingly throughout and wherein:

FIG. 1 is a block diagram illustrating the encryption system of thepresent invention;

FIG. 2 is a flow diagram of an exemplary embodiment of the method ofencrypting a block of characters in the present invention;

FIG. 3 is a “C” program implementing the exemplary embodiment of themethod of encrypting a block of characters in the present invention;

FIG. 4 is an exemplary embodiment of t1box; and

FIG. 5 is an exemplary embodiment of t2box.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The exemplary embodiment of the present invention consists of a firststation 1000 encrypting data for wireless transmission to a secondreceiving station 2000, as depicted in FIG. 1. First station 1000 can bea remote station transmitting to a second station 2000, which could be abase station. Alternatively, first station 1000 could be a base stationtransmitting to a second station 2000, which could be a remote station.In all likelihood, both remote and base stations will have encryptionand decryption means, as well as transmission and reception means, butthe simplified system shown in FIG. 1 shows clearly the elementsrequired to enable the present invention. Further, the benefits of thisinvention are not limited to wireless communications but can be readilyapplied in any situation where secure data must be transmitted over amedium which is susceptible to interception, as will be well understoodby those skilled in the relevant art.

In FIG. 1, memory 10 containing the necessary data for encryptionaccording to the BEVL algorithm of the present invention is connectedwith processor 20. In the exemplary embodiment, processor 20 is arelatively simple 8-bit microprocessor, capable of executinginstructions stored in BEVL code 19. Processor 20 contains an arithmeticlogic unit (ALU, not shown) capable of performing simple 8-bitinstructions such as bitwise exclusive OR (referred to simply as XOR ordenoted hereinafter), integer addition and subtraction, and the like.Processor 20 is also capable of general program flow instructions andthe ability to load and store values from a memory, such as memory 10.Those skilled in the art will recognize that these requirements arequite minimal, making the present invention quite suitable toapplications where size and/or cost requirements make simplemicroprocessors desirable, such as in portable devices. Clearly thepresent invention can easily be implemented using more powerfulmicroprocessors as well.

Memory 10 contains tables t1box 12 and t2box 14, an encryption key 16,and the code to be executed (BEVL code) 19. Data to be encrypted isinput to processor 20, which stores that data in memory 10 in a locationreferred to as data 18. Although FIG. 1 depicts all these elements in asingle memory, it is understood that a plurality of memory devices couldbe used. In the preferred embodiment, the tables 12 and 14 as well asBEVL code 19 are stored in non-volatile memory such as EEPROM or FLASHmemory. These portions of the memory need not be writeable.

Encryption key 16 can be generated by a number of means that are wellknown in the art. A simple embodiment may have key 16 in non-volatilememory that is programmed once at the time the station is activated forservice. In the exemplary embodiment, key 16 is generated and changedaccording to the protocol as set forth in the aforementionedEIA/TIA/IS-54-B.

The data to be encrypted, data 18, is stored in random access memory(RAM). The encryption will be performed “in place”, which means thememory locations holding the unencrypted data at the beginning ofprocedure will also hold the intermediate values as well as the finalencrypted data.

Data 18 is encrypted in processor 20 according to BEVL code 19,utilizing t1box 12, t2box 14, and encryption key 16. A description ofthe encryption process is detailed hereinafter.

Encrypted data 18 is delivered by processor 20 to transmitter 30 whereit is modulated, amplified and upconverted for transmission on antenna40.

Antenna 50 receives the data and passes it to receiver 60 where the datais downconverted, amplified, demodulated, and delivered to processor 70.In the exemplary embodiment, the format for the wireless communicationbetween the two stations depicted in FIG. 1 is described in “MobileStation-Base Station Compatibility Standard for Dual-Mode Wide BandSpread Spectrum Cellular System”, TIA/EIA/IS-95-A. The use of CDMAtechniques in a multiple access communication system such as a wirelesstelephone system is disclosed in U.S. Pat. No. 4,901,307, entitled“SPREAD SPECTRUM MULTIPLE ACCESS COMMUNICATION SYSTEM USING SATELLITE ORTERRESTRIAL REPEATERS,” assigned to the assignee of the presentinvention, and incorporated by reference herein. The use of CDMAtechniques in a multiple access communication system is furtherdisclosed in U.S. Pat. No. 5,103,459, entitled “SYSTEM AND METHOD FORGENERATING SIGNAL WAVEFORMS IN A CDMA CELLULAR TELEPHONE SYSTEM,” alsoassigned to the assignee of the present invention, and incorporated byreference herein.

Processor 70, which has the same requirements as processor 20, iscoupled to memory 80. Memory 80 is comprised of memories 82, 84, 86, 88,and 89 which are analogous to memories 12, 14, 16, 18, and 19,respectively. Processor 70 stores the encrypted data in data memory 88.Key 86 is determined in like fashion to key 16, described previously.Tables 82 and 84 are identical to tables 12 and 14. Since the dataprocessing in this invention is self-inverting, BEVL code 89, identicalto BEVL code 19, is executed in processor 70 in conjunction with t1box82, t2box 84, and key 86 on encrypted data 88, just as was done in theencryption process of data 18. As before, the data processing isperformed “in place”, and the result in data 88 will be the decrypteddata. Processor 70 retrieves the decrypted data from memory 80 anddelivers it for subsequent use through the data output. In the exemplaryembodiment, the resultant data will be used in authentication proceduresas disclosed in EIA/TIA/IS-54-B.

FIG. 2 illustrates a flow chart of the method used by processors 20 and70 in conjunction with previously described memory elements 10 and 80,respectively. As mentioned previously, the encryption process isself-inverting, meaning the decryption process is the same as theencryption process. Hence, only the encryption process will be describedin detail. The decryption process will be obvious by substituting theencrypting blocks of FIG. 1 with the analogous decrypting blocks of FIG.1 as set forth previously.

Block 99 marks the beginning of the encryption process. An array ofcharacters named buf[ ] is used to describe the characters to beencrypted as stored in data memory 18. The variable n denotes the lengthof the message to be encrypted in terms of number of characters. Asstated previously, one of the improvements present in the BEVL processis the five pass encryption that takes place. Each of the five passeshas been blocked out in dashed lines and labeled 1-5 to make them easyto distinguish. Each pass has notable similarities and differences.Passes 1, 3, and 5 use the table t1box 12 and work from the beginning ofthe buffer towards the end. Passes 2 and 4 use the table t2box 14 andwork from the end of the buffer until the beginning is reached. BEVL'sself-inverting property comes from the fact that pass 3 isself-inverting, while pass 1 is the inverse of pass 5 and pass 2 is theinverse of pass 4.

In the preferred embodiment of the present invention, the passes aremade in opposite directions. In alternative embodiments, passes couldprogress in the same direction, with alternating passes using the sameor different tables (re-using the same table in multiple passes doesmake the encryption more robust, but not as robust as when differenttables are used). Inserting additional passes is another alternativewhich can be used in combination with either approach. In the situationwhere passes are made in the same direction, modifications to the firstbuffer entry are more predictable, with predictability decreasing inmodifications further down the buffer. When alternating opposite passdirections are used, the modification to the first byte in the buffer isfairly predictable. However, the modification to that byte in the secondpass depends on all the bytes in the buffer, making it much lesspredictable. In similar fashion, the modification to the last byte inthe buffer depends on all the bytes in the buffer during the first pass,while a more predictable change is made in the second. Since thepredictability of change is distributed more evenly using passes inopposite directions, doing so is much preferable to using multiplepasses in the same direction. Note that pass 3 doesn't really have adirection, since the change made would be identical either way.

In each pass, a function tbox( ) is used. It is in this function thatkey 16 is incorporated. The parameters passed to function tbox( )consist of a 256 byte table which will either be passed t1box 12 ort2box 14, and an index labeled tv. In the exemplary embodiment, tbox( )is defined as:

tbox(B,tv)=B[B[B[B[B[B[B[B[B[tv≈k0]+k1]≈k2]+k3]≈k4]+k5]≈k6]+k7]≈k0],  (1)

where

-   -   k0 through k7 denote eight 8-bit segments which when        concatenated form the 64-bit key 16;    -   B[x] is the xth 8-bit element of an array B;    -   ≈ denotes the bit-wise exclusive OR operation; and    -   + represents modulo 256 addition.        In an alternative embodiment, where a key of a certain length        provides encryption that is considered too strong, the key        strength can be artificially limited without changing the length        of the key by altering the tbox( ) function. For example, a 64        bit key can be artificially limited to 40 bits by using the 64        bit key in such a manner that it is in an equivalence class of        2̂24 others while still ensuring that any single bit change to        the key will produce a different result. The following        definition of tbox( ) exhibits the recommended variation to        render a 64 bit key effectively a 40 bit key:

$\begin{matrix}{{{{tbox}( {B,{tv}} )} = {B\lbrack {{B\lbrack {{B\lbrack {{B\lbrack {{B\lbrack {{B\lbrack {{B\lbrack {{B\lbrack {{B\lbrack {{tv} \approx {k\; 0}} \rbrack} + {k\; 1}} \rbrack} \approx \lbrack {{k\; 2} \approx {k\; 3}} )} \rbrack} + ( {{k\; 2} \approx {k\; 3}} )} \rbrack} \approx ( {{k\; 4} \approx {k\; 5}} )} \rbrack} + \lbrack {{k\; 4} \approx {k\; 5}} )} \rbrack} \approx ( {{k\; 6} \approx {k\; 7}} )} \rbrack} + ( {{k\; 6} \approx {k\; 7}} )} \rbrack} \approx {k\; 0}} \rbrack}},} & (2)\end{matrix}$

where

-   -   k0 through k7 denote eight 8-bit segments which when        concatenated form the 64-bit key 16;    -   B[x] is the xth 8-bit element of an array B;    -   ≈ denotes the bit-wise exclusive OR operation; and    -   + represents modulo 256 addition.

The tbox( ) function is designed such that each of the intermediateoperations are permutations, meaning each input has a one-to-one mappingto an output. In the exemplary embodiment, the operations used aremodulo 256 addition and logical exclusive OR. If the input value passedto tbox( ) is a permutation, and the table lookup is as well, the use ofthese functions guarantees that the output of tbox( ) will also be aone-to-one function. In other words, the tbox( ) function as a whole isguaranteed to be a permutation if the table passed to it also is. Thisis not the case for CMEA, where the steps in the tbox( ) function arenot one-to-one. Therefore, in CMEA, even if the CAVE table, which is nota permutation, were to be replaced with a table which is a permutation,the output of tbox( ) still would not be a permutation. Conversely forBEVL, any choice of one-to-one functions for combining key material togenerate the final permutation would be acceptable. The exemplaryembodiment is one such method. Alternative methods can easily besubstituted by those skilled in the art which still conform to thispermutation principle of the present invention. Intermediate functionswhich do not preserve the one-to-one nature of the output canalternatively be employed in the BEVL tbox( ) function, but the resultswould be sub-optimal.

A further improvement included in the definition of tbox( ) is that someof the key bits are used both at the beginning and at the end. In theexemplary embodiment key byte k0 is used, but alternative embodimentscan employ any of the key bits and accomplish the same improvement. Theuse of the same value defeats the meet-in-the-middle attack. Failing toreuse at least some of the key information at both the beginning and endallows a straightforward, albeit computationally complex, derivation ofthe key from a small number of values of the tbox( ) function. With thisreuse, tables used in efforts to attack the encryption require much morespace and computations required to find a solution are much moreextensive.

The exemplary embodiment of BEVL details the use of the tbox( ) functionin conjunction with the two tables t1box and t2box The resultant outputsare key-dependent permutations of the possible inputs. However, sincethe values of the function depend only on the key, not on the data, thefunction can alternatively be pre-computed for the 256 possible inputsand two possible tables with the results stored in memory. Thus a tablelook up can replace the reevaluation of the function. Those skilled inthe art will recognize that these two methods are functionallyequivalent, and will be able to make the time versus space tradeoff whenemploying an embodiment of the present invention. An equivalentalternative is to start with tables initialized with a permutation ofthe 256 possible inputs, and perform a key-dependent shuffling of thosetables when the key is initialized. Then, during subsequent encryption,a table index operation would be used instead of the current calls totbox( ), with equal effect.

The tables t1box and t2box are strict permutations, where no entry inthe table is equal to its index. This strictness guarantees that thereexists no key which is weaker than any other key by allowing anintermediate value in a tbox( ) computation to remain unchanged. Thefact that the tables are permutations is important, as describedpreviously in reference to function tbox( ). If the tables were notpermutations, then after the table lookup in the tbox( ) function, therewould be some values which could not be the result. These impossiblevalues would allow guesses for return values from tbox( ) and parts ofthe key to be eliminated, reducing the work to guess the 64 bit keysignificantly. Alternative embodiments could employ tables which are notpermutations, but the encryption would be sub-optimal.

Any form of cryptanalysis of CMEA must begin by deriving values of thetbox( ) function. A complete analysis, where all outputs for the 256possible inputs are known, allows CMEA to be applied even withoutknowing the initial key. However, recovery of the key is possibleknowing as few as four distinct values of the function. Thus BEVL placesemphasis on disguising the outputs from tbox( ) with other outputs,particularly the value of tbox(0). A number of alternatives areenvisioned to accomplish this disguise. The preferred embodiment uses asecond different table, t2box, and an added pair of passes each whichare performed in opposite directions. Any of these three modifications,or sub-combinations thereof, would address the problem to some extent.However, the combination of all three provides the most security.

In the preferred embodiment, the forward and backward passes usedifferent tables, t1box and t2box, in conjunction with the tbox( )function. This is done so that cryptanalysis would require discovery oftwo complementary sets of function values, rather than just one set.Since the passes tend to disguise each other, two tables provide thebest security. Alternative embodiments are envisioned which employ onlya single table. While these methods are still secure, they are lesssecure than those where two tables are employed.

Begin pass 1 by proceeding from block 99 to block 102, where variable vand buffer index i are initialized to zero. Then, in block 104, eachcharacter buf[i] is modified by adding to itself the result of functioncall tbox(t1box, v≈i). The variable v is subsequently updated by XORingitself with the new value of buf[i]. The buffer index i is thenincremented. In block 106, if i<n, the pass is not complete and flowreturns to block 104. When all characters have been modified accordingto block 104, i will equal n and pass 1 will be complete. Note that thecharacters were modified beginning with buf[0] working towards the end,buf[n−1].

Begin pass 2 by proceeding from block 106 to block 202, where variable vis initialized to the value n and buffer index i is initialized to thevalue n−1. Then, in block 204, each character buf[i] is modified byadding to itself the result of function call tbox(t2box, v≈i). Thevariable v is subsequently updated by XORing itself with the new valueof buf[i]. The buffer index i is then decremented. In block 206, if i≧0,the pass is not complete and the flow returns to block 204. When allcharacters have been modified according to block 204, i will equal −1and pass 2 will be complete. Note that, unlike pass 1, the characterswere modified beginning with buf[n−1] working towards the beginning,buf[0], and the table t2box 14 was used instead of table t1box 12.

Pass 3 begins in block 302. Buffer index i is initialized to zero.Variable v is not used in this pass. Then, in block 304, each characterbuf[i] is modified by XORing with itself the result of function calltbox(t1box, i+1). The buffer index i is then incremented. In block 306,if i<n, the pass is not complete and the flow returns to block 304. Whenall characters have been modified according to block 304, i will equal nand pass 3 will be complete. Note that, like in pass 1, the characterswere modified beginning with buf[0] working towards the end, buf[n−1],and table t1box 12 was used. As stated before, however, the direction ofpass 3 is not important, since the identical result is achieved witheither direction.

In pass 3, a different output from tbox( ) is combined with each buf[ ]entry. Because the outputs from tbox( ) form a permutation, at most onlyone such value can possibly be zero. Whether or not there will be a zerodepends on the key. In BEVL, the change in the buffer is key-dependentand very difficult to predict. On average, the chance that one of thevalues will be zero is n/256, where n is the length of the buffer. Anyself-inverting key-dependent or data-dependent change which guaranteesthat the values in the buffer will be altered is sufficient to ensureencryption. This is an important improvement for BEVL, since, in CMEA,values which remain unchanged lead to cases where the algorithm fails toencrypt at all.

Begin pass 4 by proceeding from block 306 to block 402, where variable vis initialized to n and buffer index i is initialized to the value n−1.Then, in block 404, a temporary variable t is assigned the valuereturned by the function call tbox(t2box, v≈i). The variable v issubsequently updated by XORing itself with the current value of buf[i].Each character buf[i] is then modified by subtracting from itself thevalue of temporary variable t. The buffer index i is then decremented.In block 406, if i≧0, the pass is not complete and the flow returns toblock 404. When all characters have been modified according to block404, i will equal −1 and pass 4 will be complete. Note that, like inpass 2, the characters were modified beginning with buf[n−1] workingtowards the beginning, buf[0], and table t2box 14 was used.

Begin pass 5 by proceeding from block 406 to block 502, where variable vand buffer index i are initialized to the value zero. Then, in block504, a temporary variable t is assigned the value returned by thefunction call tbox(t1box, v≈i). The variable v is subsequently updatedby XORing itself with the current value of buf[i]. Each character buf[i]is then modified by subtracting from itself the value of temporaryvariable t. The buffer index i is then incremented. In block 506, ifi<n, the pass is not complete and the flow returns to block 504. Whenall characters have been modified according to block 504, i will equal nand pass 5 will be complete. Note that, like in passes 1 and 3, thecharacters were modified beginning with buf[n−1] working towards thebeginning, buf[0], and table t1box 12 was used.

Proceed now to block 600. Encryption is now complete. Ball now containsthe encrypted characters for secure transmission.

A “C” program implementing the operation described above is provided inFIG. 3. Table t1box 12 is provided in “C” in FIG. 4. Table t2box 14 isprovided in “C” in FIG. 5.

The previous description of the preferred embodiments is provided toenable any person skilled in the art to make or use the presentinvention. The various modifications to these embodiments will bereadily apparent to those skilled in the art, and the generic principlesdefined herein may be applied to other embodiments without the use ofthe inventive faculty. Thus, the present invention is not intended to belimited to the embodiments shown herein but is to be accorded the widestscope consistent with the principles and novel features disclosedherein.

1. A method for encrypting data, the method comprising: first encodingthe data in accordance with a keyed transformation; and second encodingthe first encoded data; wherein the first keyed transformationcomprising selecting an entry from a first table in accordance with afirst index and wherein the first table has no entry equal to itscorresponding index.
 2. The method of claim 1, wherein the first keyedtransformation is a non-linear transformation.
 3. The method of claim 1,wherein the second encoding comprises encoding in accordance with asecond keyed transformation, and wherein the second keyed transformationcomprises selecting an entry from a second table in accordance with asecond index and wherein the second table has no entry equal to itscorresponding index.
 4. The method of claim 3, further comprising third,fourth, fifth and sixths encodings.
 5. The method of claim 1, wherein atleast one of the first index and second index is a portion of a key. 6.An apparatus for encrypting data, the apparatus comprising: a memoryconfigured to store data to be encrypted; and a processor configured tofirst encode the data in accordance with a first keyed transformationcomprising a table lookup using an index value, wherein no entry in thetable is equal to its corresponding index; and second encode the firstencoded data.
 7. The apparatus of claim 1, wherein the keyedtransformation is a non-linear transformation.
 8. The apparatus of claim1, wherein the processor performs the second encoding in accordance witha second keyed transformation comprising selecting an entry from asecond table in accordance with a second index and wherein the secondtable has no entry equal to its corresponding index.
 9. The apparatus ofclaim 8, wherein the processor is further configured to perform fouradditional encodings.
 10. The apparatus of claim 1, wherein at least oneof the first and second indexes is a portion of a key.
 11. Acomputer-program product for wireless communications, comprising: acomputer-readable medium comprising code for: first encoding data inaccordance with a keyed transformation; and second encoding the firstencoded data; wherein the first keyed transformation comprisingselecting an entry from a first table in accordance with a first indexand wherein the first table has no entry equal to its correspondingindex.
 12. The apparatus of claim 1, wherein the keyed transformation isa non-linear transformation.
 13. The apparatus of claim 1, wherein theprocessor performs the second encoding in accordance with a second keyedtransformation comprising selecting an entry from a second table inaccordance with a second index and wherein the second table has no entryequal to its corresponding index.
 14. The apparatus of claim 1, whereinat least one of the first and second indexes is a portion of a key. 15.An apparatus for encrypting data, the apparatus comprising: means forstoring data to be encrypted; and means for first encoding the storeddata in accordance with a first keyed transformation comprising a tablelookup using an index value, wherein no entry in the table is equal toits corresponding index; and means for second encoding the first encodeddata.